Problem: Solve for $x$ and $y$ using substitution. ${2x+y = -7}$ ${y = -3x-11}$
Solution: Since $y$ has already been solved for, substitute $-3x-11$ for $y$ in the first equation. ${2x + }{(-3x-11)}{= -7}$ Simplify and solve for $x$ $2x-3x - 11 = -7$ $-x-11 = -7$ $-x-11{+11} = -7{+11}$ $-x = 4$ $\dfrac{-x}{{-1}} = \dfrac{4}{{-1}}$ ${x = -4}$ Now that you know ${x = -4}$ , plug it back into $\thinspace {y = -3x-11}\thinspace$ to find $y$ ${y = -3}{(-4)}{ - 11}$ $y = 12 - 11$ $y = 1$ You can also plug ${x = -4}$ into $\thinspace {2x+y = -7}\thinspace$ and get the same answer for $y$ : ${2}{(-4)}{ + y = -7}$ ${y = 1}$